We consider the problem of communicating a sequence of concepts, i.e., unknown and potentially stochastic maps, which can be observed only through examples, i.e., the mapping rules are unknown. The transmitter applies a learning algorithm to the available examples, and extracts knowledge from the data by optimizing a probability distribution over a set of models, i.e., known functions, which can better describe the observed data, and so potentially the underlying concepts. The transmitter then needs to communicate the learned models to a remote receiver through a rate-limited channel, to allow the receiver to decode the models that can describe the underlying sampled concepts as accurately as possible in their semantic space. After motivating our analysis, we propose the formal problem of communicating concepts, and provide its rate-distortion characterization, pointing out its connection with the concepts of empirical and strong coordination in a network. We also provide a bound for the distortion-rate function.

翻译：我们考虑一组概念（即未知且可能随机的映射，仅能通过样本观测到，映射规则未知）的序列通信问题。发送端对可用样本应用学习算法，通过优化一组模型（即已知函数）上的概率分布从数据中提取知识，这些模型能更好地描述观测数据，从而可能揭示潜在的概念。随后，发送端需要通过速率受限信道将学习到的模型传输至远程接收端，使接收端能够在语义空间中解码出尽可能准确描述底层采样概念的模型。在阐明研究动机后，我们正式提出概念通信问题，给出其率失真表征，指出其与网络中经验协调和强协调概念的联系，并给出失真率函数的界。